The Swiss defeated the world number one in four sets on Sunday to clinch the first Grand Slam title of his career.
"It's the best Grand Slam ever," he told reporters. "I still don't know whether I'm dreaming or not.
"I'm sorry for you, Rafa. You're a great friend and an amazing champion. It's always a pleasure to play against you. Well done on your comeback."
Wawrinka's victory at the tournament has seen him move up to third place in the world rankings.